Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

In gauge theories with continuous groups there exist classical solutions whose energy vanishes in the thermodynamic limit (in any dimension). The existence of these super-instantons is intimately related to the fact that even at short distances perturbation theory can fail to produce unique results. This problem arises only in non-Abelian models and only starting at O(1/beta^2).Comment: 9 pages, 1 figure available on request from the author

Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

In dimension $D\leq 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at $O(1/\beta^2)$. This effect modifies the $\beta$-function of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.Comment: 8 pages, plain LaTeX, MPI-Ph/93-87 and AZPH-TH/93-3

Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be $O(1)$ and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the so-called super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called 'perfect actions'. It also shows that David's recent claim that super-instanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.Comment: 14 pages, latex, no figure

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number $n$ in the range between 25 and 35, have been deflected by 90$^\circ$, decelerated and loaded into off-axis electric traps at initial densities of $\approx 10^6$ atoms/cm$^{-3}$ and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 K and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as $n^{-4}$ and corresponding closely to the natural lifetimes of the initially prepared Rydberg-Stark states. The decay rate was found to continually decrease over time and to reach an almost $n$-independent rate of more than (1 ms)$^{-1}$ after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. TheComment: 36 pages, 18 figure

Adaptive stepsize and instabilities in complex Langevin dynamics

Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive stepsize in complex Langevin simulations and find that unstable trajectories are completely eliminated. To illustrate the generality of the approach, we apply it to the three-dimensional XY model at nonzero chemical potential and the heavy dense limit of QCD.Comment: 12 pages, several eps figures; clarification and minor corrections added, to appear in PL

No-go theorem on spontaneous parity breaking revisited

An essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories concerns the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source. We show how this requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.Comment: Talk presented at LATTICE99(Theoretical Developments),3 pages. Latex using espcrc2.st

Emergency Preparedness and Response Protocol in South Dakota Public Schools

Providing a safe and secure learning environment is one of the most important components of being a superintendent. This quantitative study examined school superintendent perceptions of safety and the importance of four emergency crisis components, prevention, preparedness, response, and recovery in the state of South Dakota. The study was included 147 school public school districts in South Dakota and two school districts were excluded because they were only K-8 school districts. The study also investigated the relationship of school size and its affect on school safety based on superintendent perceptions of the four components of emergency crisis plans. The results show a discrepancy between the importance placed on the four emergency crisis components by superintendents and their perceptions of safety based on the four components. The results show a discrepancy between the importance placed on the four emergency crisis components by superintendents and their perceptions of safety based on the four components. The research shows statistical significance between (r[81]= 12.66, p\u3c.05) prevention, (r[81]= 11.84, p\u3c.05) preparedness, (r[81]= 12.60, p\u3c.05) response, and (r[81]= 9.21, p\u3c.05) recovery between the size of the school district and the superintendents perceptions of safety for their school. The data showed larger school districts are perceived as being safer based on superintendent perceptions. The data showed the importance of each emergency crisis plan component and the effect of school size on superintendent perceptions of safety